Work on Moduli and Geometric Invariant Theory (except Abelian Varieties)
Moduli spaces are essentially maps. In an ordinary map, a point on a piece of paper corresponds to a location on the earth. Similarly, a point in a moduli space corresponds to an object of some kind, a variety or bundle or something more elaborate. The set of all these objects is thus put together in this fine but rather intangible 'map' known as a moduli space. That's why I have put a map of part of Maine in the background.
- An Elementary theorem in Geometric Invariant Theory, Bull. Amer. Math. Soc., 1961, pp. 483-487. Scanned reprint and DASH reprint
- Topics in the Theory of Moduli, (published in Japanese), Sugaku , 1963. Scanned English manuscript
- Projective Invariants of Projective Structures, International Congress of Mathematicians, Stockholm 1962, 1963, pp. 526-530. Scanned reprint
- The Boundary of Moduli Schemes, mimeographed notes from the 1964 Woods Hole Symposium on Algebraic Geometry. Scanned manuscript
- Picard Groups of Moduli Problems, in Arithmetic Algebraic Geometry, (Proceedings of a Conference in Purdue, 1963), Harper and Row, 1965. Scanned reprint
- Two Fundamental Theorem on Deformations of Polarized Varieties (with T. Matsusaka), Amer. J. of Math., 1964, pp. 668-684. Scanned reprint and DASH reprint
- Geometric Invariant Theory, Springer-Verlag, 1965; 2nd enlarged edition, (with John Fogarty), 1982; 3rd enlarged edition, (with Frances Kirwan and John Fogarty), 1994, DejaVu
- Abelian Quotients of the Teichmuller Modular Group, Journal d'Analyse, 1967, 28, pp. 227-244. Scanned reprint
- Periods of Moduli Spaces of Bundles on Curves (with P. Newstead), Amer. J. of Math., 1968, 90, pp. 1200-1208. Scanned reprint and DASH reprint
- The Irreducibility of the Space of Curves of Given Genus (with P. Deligne), Publ. Math. de l'I.H.E.S., 1969, 36, pp. 75-109. Scanned reprint and DASH reprint
- A Remark on Mahler's Compactness Theorem, Proc. Amer. Math. Soc., 1971, 28, pp. 289-194. Scanned reprint and DASH reprint
- The Structure of the Moduli Spaces of Curves and Abelian Varieties, Actes du Congress Int. du Math., Nice, 1970; Gauthier-Villars, 1971. Scanned reprint
- Introduction to the Theory of Moduli (with K. Suominen), in Algebraic Geometry, Oslo 1970 F. Oort editor, Wolters-Noordhoff, 1972, pp. 171-222.Scanned reprint
- Matsusaka's Big Theorem (with D. Lieberman), in Algebraic Geometry, Arcata 1974, AMS Proc. of Symposia in Pure Math., 29, 1975, pp. 513-530. Scanned reprint
- The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "Div" (with F. Knudsen), Math. Scand., 39, 1976, pp.19-55.
The projectivity of the moduli space of stable curves, II: the stacks Mg,n (sequel by F. Knudsen), Math. Scand., 52, 1983, pp.161-199.
The projectivity of the moduli space of stable curves III: the line bundles on Mg,n and a proof of trhe projectivity of the completion of Mg,n in characteristic 0 (sequel by F. Knudsen), Math. Scand., 52, 1983, pp.200-212. Scanned reprint
- Stability of Projective Varieties, Monographie No. 24 de L'Enseignement Math., 23, 1977, pp. 39-110. Scanned reprint
- On the Kodaira Dimension of the Moduli Space of Curves (with Joe Harris and an appendix by William Fulton), Inv. Math., 1982, pp.23-88. Scanned reprint and DASH reprint
- Towards an Enumerative Geometry of Moduli Space of Curves, in Arithmetic and Geometry, edited by M. Artin, J. Tate, Birkhauser-Boston, 1983, pp.271-326. Scanned reprint
- A Stratification of the Null Cone via the Moment Map (with Linda Ness), Amer. J. of Math., 106, 1984, pp.1281-1329. Scanned reprint and DASH reprint